In one lottery, a player wins the jackpot by matching all five numbers drawn from white balls (1 through 45 ) and matching the number on the gold ball (1 through 35 ). If one ticket is purchased, what is the probability of winning the jackpot?

the probability of winning the jackpot is 1 in 42 761 565.

Step-by-step explanation:

The number of ways to select five numbers from 45 is:

ⁿCₐ = n! / (n - a) ! * a!

where

a is the number of objects n is the number of distinct objects

Therefore,

⁴⁵C₅ = 45! / (45 - 5) ! * 5!

= (45 * 44 * 43 * 42 * 41) / (5 * 4 * 3 * 2 * 1)

= 1221759

There are 35 ways to select a gold ball. Therefore, the total number of ways to get 6 matching numbers is:

1221759 * 35 = 42 761 565